1. Field of the Invention
The invention relates to the field of analyzing the properties of electrolytes and testing the performance of electrochemical processes. The invention focuses on electroplating processes, although it can also be directly applied to other electrolytic processes including, but not limited to, electrowinning, electrorefining, and anodizing.
2. Background of the Invention
The performance of electrochemical systems depends on the design of the cells in which the electrochemical reactions take place and on the appropriate selection of the operating conditions, including current, voltage, electrolyte composition, species concentrations, flow, etc., to produce the desired results. The selection of the operating conditions is particularly critical in plating cells where the deposit thickness distribution and properties (e.g., appearance, color, surface texture, adhesion, and composition) strongly depend on the cell configuration and the process parameters. In order to obtain adequate quality product, practitioners often utilize two approaches: (i) experimental—a test fixture or apparatus e.g., the “Hull cell” [described e.g., in U.S. Pat. Nos. 2,149,344, 2,801,963, 3,121,053] is used to generate, by specifying and controlling the total current, a sample that is plated under a range of current densities. The sample is visually inspected and correlated with the process conditions; (ii) modeling—where the electrochemical process is mathematically analyzed and the conditions to produce the desired results are sought. In recent years, the latter approach has been enhanced by simulations using computer-aided-design (‘CAD’) software e.g., Cell-Design® [Ref. 1]. Knowing the process parameters (e.g., kinetics constants, standard potential, and conductivity) is an essential pre-requisite for the modeling approach. Yet, this data is typically not available, particularly not for commercial electrolyte formulations, and generating this data is quite onerous.
As discussed below, both these approaches (‘experimental deposition onto a test fixture’ and ‘modeling’) suffer at present from a number of shortcomings that the invention disclosed herein resolves.
Limitations of the Current Approaches:
A. Limitations of Special Fixtures and Devices that Characterize Deposits Produced Under a Range of Current Densities
The most commonly used device to experimentally explore a deposit produced under a range of current densities is the ‘Hull cell’ [U.S. Pat. Nos. 2,149,344, 2,801,963, 3,121,053]. The Hull cell, shown in FIG. 1A, is a prismatic cell with vertical insulating sidewalls, an anode panel (2) and a slanted cathode panel (3). Due to the different angles of the corners between the slanted cathode and its neighboring insulating sidewalls (acute angle (4) at one side of the cathode and an obtuse angle (5) at the other side), and the varying distance between regions on the cathode and the anode, the deposit is plated on the cathode under a non-uniform current density: the highest current density (and correspondingly, the thickest deposit) is near the corner with the obtuse angle (5); the lowest current density (and thinnest deposit) is next to the corner with the acute angle (4). The current density and the corresponding deposit thickness vary between the two corners in a non-linear fashion. Since, only the total current to the entire cathode can be measured in the Hull cell, users are given a scale (6), shown in FIG. 1B, on which the expected current density is indicated as a function of position. By placing this scale alongside the cathode panel (3), as shown in FIG. 1B, users can estimate the current density that corresponds to the deposit at the given location. The major deficiency of the Hull-cell is that the current density indicated on the scale is only a rough approximation. This approximation is inherent and cannot be improved because the current distribution does not depend only on the cell geometry, as implied in the Hull-cell description, but it varies with the type of plating solution used. For example, lead and zinc deposition produce a highly non-uniform distribution; copper plating produces a moderately uniform distribution, and nickel, iron and gold produce significantly more uniform distribution. The curves displayed in FIG. 2 show the computed current density distributions in typical electrolytes (copper from acidified copper sulfate, and Watts-type nickel), as modeled by Cell-Design© CAD software, in comparison to the corresponding value indicated by the Hull cell scale. As noted in FIG. 2, even for those very common electrolytes, significant differences (exceeding 25%) at the low and high current density ranges exist. An even more serious obstacle to using the Hull cell for the selection of the proper operating conditions is the variation of the current distribution due to variations in the electrolyte's temperature, ionic concentrations, conductivity, additive concentration, contaminants and by-products, which are supposed to be analyzed by the Hull cell test, yet their effects on the current density is not indicated. Accordingly, there exists a significant uncertainty in matching the deposit at any given location along the Hull-cell cathode to the actual prevailing local current density. Furthermore, the deposit thickness varies gradually and continuously along the cathode. Since the user relies on visual inspection of the deposit to determine whether the appearance of the latter is satisfactory, it is difficult to clearly differentiate the acceptable range.
Another device that is occasionally used to determine the properties of the plating electrolyte is the Haring-Blum cell. Here, two parallel cathodes are positioned at two different distances, on both sides of a common anode. The ratio of the deposit weights on the cathodes characterizes the throwing power of the electrolyte, which is proportional to the ratio between the deposition reaction resistance and the electrolyte resistance. While the Haring Blum cell provides the throwing power (or the resistance ratio) at only one current density in each experiment, there is a need to provide this ratio across a broad range of current density in a single experiment.
Two variations on the Hull cell have been subsequently suggested. One is the Casey-Asher cell which has an elongated rectangular cross-section, where the non-uniform deposition takes place along one of the elongated electrodes. The second is the pie-shaped Tena cell, consisting of two concentric cylindrical insulating walls bound by two radially positioned planar electrodes. Both of the variations on the Hull cells, while not widely used, suffer from the same deficiencies as the Hull cell.
More recently, Abys et. al. introduced the ‘hydro dynamically modulated Hull cell’ [Ref. 2 and U.S. Pat. Nos. 5,228,976 and 5,413,692], which was designed to provide improved and better quantified mass transport. The cell consists of a cylindrical rotating cathode and an anode positioned to provide a non-uniform current distribution. Specially positioned baffles help adjust the current distribution. This cell suffers from the same limitations that apply to the Hull cell, i.e., it provides a distribution that depends on the electrolyte type and composition, and not just on the geometry. Furthermore, since only the total current is measurable, the deposit at any given location along the cathode cannot be precisely associated with a specific current density. Another very similar cell that has recently been introduced by Landolt and Madore [Ref. 3], has identical features to Abys' et. al. cell and suffers from the same shortfalls.
None of the cells described above provides any quantitative information concerning the physical and/or chemical parameters of the process.
B. Difficulty in Obtaining Electrochemical Process Parameters
A major impediment to applying quantitative modeling (both analytical and computer-aided design) to electrochemical systems is the paucity of available property data that such modeling requires. Typically, thermodynamic, kinetics, and transport properties are needed in order to characterize the processes that take place in electrochemical cells. These processes can be generally divided into two major categories: (a) processes associated with the electrode reactions and (b) ionic transport in the electrolyte.
The electrode processes are quite complex and typically involve numerous steps that are difficult to unravel. Their characterization can, however, be accomplished without detailed mechanistic knowledge by specifying the global thermodynamics and kinetics parameters. However, obtaining this data is typically quite difficult. The thermodynamics properties include the standard reaction potential (E0) whose value can be found in standard thermodynamic tables. However, the actual equilibrium potential (E) depends also on the temperature, the electrolyte concentration (ionic activities) and particularly on the composition, including species that complex the reacting ion and that modify the adsorption properties on the electrode. Determination of the effects of all these parameters is quite difficult and requires at the bare minimum the use of a special, well characterized, reference electrode [Refs. 4, 5]. Specification of the electrode kinetics requires a polarization curve that describes the dependence of the electrode overpotential (=potential exceeding the equilibrium potential due to irreversible dissipative processes, e.g., kinetics resistance) as a function of the current density. Commonly, the polarization curve is represented in terms of the Butler-Volmer equation, which has some fundamental justification, but in practice serves mostly as a correlation, i.e., the parameters are determined empirically through polarization experiments. Although the physical significance of the parameters in this equation can be attributed only in very few simple processes, the general form of this equation and its three adjustable parameters (exchange current density [i0], anodic [α]and cathodic [β] transfer coefficients) that are measured empirically, have enabled to model numerous electrochemical processes. The general application of the Butler-Volmer equation, or other polynomial correlations that have been suggested, from data in the literature is, however, limited because of the interdependence of the electrode kinetics on the transport, and particularly on the reactant (and additives) concentration at the surface. These in turn, depend not only on the convective and diffusive transport but also on the current density, both of which typically vary along electrodes and with operating conditions.
Ionic transport in the electrolyte involves diffusion, migration and convection. Its simulation requires knowing the ‘integral’ diffusion coefficient of the reacting species. The latter can be measured on a rotating disk electrode assembly as introduced by Venjamin Levich in his book “Physicochemical Hydrodynamics” published by Prentice-Hall, Englewood Cliffs, N.J., 1962, which is incorporated herein by reference [6]. The experimental set-up is, however, costly. It requires a rotating disk electrode assembly, a power supply with current/voltage ramp capability and data recording capability. The process of generating the data is time consuming, and requires expertise as described, e.g., in a paper by Uziel Landau, “Determination of Laminar and Turbulent Mass Transport Rates in Flow Cells by the Limiting Current Technique”, AICHE Symposium Series 204, Vol. 77, pp. 75-87, 1981, which is incorporated herein by reference [7]. In addition, one needs to characterize the mass transport process in the cell. This typically amounts to specifying the mass transport boundary layer thickness, and its distribution in the cell, or equivalently, the limiting diffusion current. These are quite difficult to determine since they depend on detailed characterization of the flow in the cell and on the cell configuration, typically requiring computational fluid dynamics modeling. Even where forced convection is not present or is not dominant, determining the characteristics of the diffusion flux in complex geometries is difficult.
Ionic transport also proceeds via electric migration that is characterized by the conductivity. The latter varies with the electrolyte composition, concentration (i.e. it is affected by the local current density or concentration gradients), and temperature.
In addition to the difficulty in characterizing the details of the electrochemical process so that proper parameters can be assigned, there is a difficulty in obtaining the data and in particular, the kinetics parameters (e.g., i0, α and β, as described above). The literature typically offers only rate constants for pure elements (and even those are given for only one standard concentration or activity). Practical processes, and in particular plating systems, employ complex chemistries, incorporating additives and complexing agents that strongly affect the deposition kinetics, as described e.g. by U. Landau et. al., in U.S. Pat. No. 6,113,771. It is therefore required in almost all practical situations to experimentally measure the parameters for the given system. Such measurements require, however, special cells that are specifically designed for the type of measurement. Examples include conductivity cells coupled with high frequency analyzer for conductivity measurement, and rotating disk electrode for measurements of diffusivity. The rate constants, i0, α and β, must be typically obtained by conducting a sweep of a current-potential scan in cells that are difficult to design because of the requirement for (a) a uniform current density on the tested electrode (otherwise a meaningless average is detected), (b) uniform and tractable transport rates to the electrode, (c) means of detecting and subtracting the ohmic and concentration overpotentials, and (d) a three electrode system incorporating a reference electrode so that the potential of the test electrode can be elucidated. Special and costly power supplies (‘potentiostats’) that are capable of three-electrode voltage control versus a reference electrode are also required. The kinetics constants are typically extracted from polarization curves, hence a dynamic measurement in which the cell voltage or current are ramped by the power supply over sufficiently wide range must be implemented. These experimental procedures are described in the literature, e.g., in a book by Allen Bard and Larry Faulkner, “Electrochemical Methods” published by John Wiley & Sons, NY, 1980, which is incorporated herein by reference [5]. The special experimental techniques require procedures that many practical engineers are not proficient in, nor have the time to learn and carry out.